## Description

Problem 1

Suppose we have the following data:

Group 1: 4, 12+, 15, 21+, 23

Group 2: 2, 6+, 8+, 10, 19

Test H0 : h1(t) = h2(t) for all t, H1 : h1(t) 6= h2(t) for some t using the log-rank

test.

(Optional, PhD required) Please also do the calculation by hand, and check

your result.

Problem 2

Consider the kidtran dataset in the KMsurv package where the death times of

kidney transplant patients are reported. The patients can be classied by race

(1=white and 2=black) and gender (1=male and 2=female) into one of four

groups. Compare the survival curves for dierent races in each sex group.

Problem 3

Consider the larynx data in the KMsurv package. Let

Z1 = 1 if the patient is in stage II, 0 otherwise

Z2 = 1 if the patient is in stage III, 0 otherwise

Z3 = 1 if the patient is in stage IV, 0 otherwise

Z4 = age of the patient (in years):

Fit a proportional hazards model using the covariates Z1, Z2, Z3, Z4 and the

interaction term Z1 * Z4. Explain your results.

What is the relative risk of

dying for a stage II patient of age 50 as compared to a stage I patient of the

same age?